are called "off the mass shell". have a non-classical relationship between kinetic energy and mass. can have negative momentum. can have any speed.

VIRTUAL PARTICLES •

Virtual particles do not obey m2 c4 = E2 - p2 c2 and so o o o o

•

tend to destructively interfere over long distances. have a range limited by the uncertainty principle. Higher masses yield shorter distance. defined directly only in perturbation theory

The further off the mass shell a virtual particle is, the less their probability amplitude in many QM calculations.

VIRTUAL PARTICLES: DO THEY CONSERVE ENERGY? Yes, no, and controversial. Yes, • real particles that are affected by virtual particles may conserve energy. • once created, a virtual particle has a definite energy that does not change. • when being created, the energy might be considered as borrowed from a neighboring real particle.

VIRTUAL PARTICLES: DO THEY CONSERVE ENERGY? No, • virtual particle energy could be considered to arrive from nowhere, but can't be directly detected because of the uncertainty principle. Controversial, • the existence of virtual particles is "interpreted" from a mathematical framework, and some interpretations do vary.

VIRTUAL PARTICLES: UNCERTAINTY PRINCIPLE

Virtual particles are completely hidden by the uncertainty principle, living on "other side" such that Δx Δp < h. When a real particle accelerates, some of its "virtual cloud" is sufficiently accelerated that Δx Δp > h and so "become" real.

VIRTUAL PARTICLES: LAMB SHIFT The Lamb shift is •

a slight shift in the energy levels of orbiting electrons in a hydrogen atom.

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caused by an interaction between an orbiting electron and surrounding virtual electrons and photons.

•

a unique test of virtual particles in QED.

VIRTUAL PARTICLES: CASIMIR EFFECT The Casimir Effect • was discovered by Casimir while studying why mayonnaise flowed so slowly. • allows parallel plates to attract when no classical force indicates that they should. • attributed to virtual particles destructively interfering when constrained between boundaries. The zero point energy of the vacuum is changed. • can be attractive or repulsive.

VIRTUAL PARTICLES: ATTRACTIVE FORCE?

If forces result from exchanging virtual particles, and their corresponding real particles always have positive mass, how can any force be attractive? Virtual particles can carry negative momentum. Interference with other virtual photons (of the other particle) can determine attractive or negative momentum. The math is very complicated. You would need to study quantum electrodynamics.

VIRTUAL PARTICLES: CAN THEY GO FASTER THAN LIGHT? Yes, virtual particles can be considered to go faster (and slower) than light, but in doing so they are constrained not to allow FTL communication. Example: Two well separated observers would measure fluctuations in a field that could only be found to be correlated at a later time.

VIRTUAL PARTICLES: BLACK HOLE GRAVITY How does gravity get out of a black hole? • • •

Not a problem in General Relativity because there are no real or virtual particles being exchanged. Some gravity could come from matter that has not yet fallen in. In quantum gravity, virtual particles could go faster than light and so many are not constrained by the event horizon. o

But they can't carry messages FTL.

"ALL PHOTONS ARE VIRTUAL PHOTONS" • • • •

A statement (author unclear) that is still being debated. Since photons travel at c, they experience no passive of time between emission and absorption. Treated as mathematically similar in many quantum calculations. Real particles can trigger real detectors, but virtual particles can only transmit force.